70 adults and 100 children attended the carnival.
Step-by-step explanation:
Given,
Cost of each adult ticket = $10
Cost of each child ticket = $5
Total tickets sold = 170
Total revenue generated = $1200
Let,
Number of adults = x
Number of children = y
According to given statement;
x+y=170 Eqn 1
10x+5y=1200 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]
Putting y=100 in Eqn 1
[tex]x+100=170\\x=170-100\\x=70[/tex]
70 adults and 100 children attended the carnival.
Keywords: linear equation, elimination method
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Which equation represents a proportional relationship?
y=2x2
y = 4x - 2
y= 1/2x +3
y=5x
Answer:
D: y = 5x
Step-by-step explanation:
According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality. So the only one in that form would be the y = kx.
The constant k = 5
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
127 children and 264 adults swam at the public pool that day
Solution:
Let "c" be the number of children swam
Let "a" be the number of adult swam
Cost for each children = $ 1.25
Cost for each adult = $ 2.25
391 people used the public swimming pool
Therefore,
c + a = 391
a = 391 - c ------- eqn 1
The receipts for admission totaled $752.75
Therefore, we frame a equation as:
number of children swam x Cost for each children + number of adult swam x Cost for each adult = 752.75
[tex]c \times 1.25 + a \times 2.25 = 752.75[/tex]
1.25c + 2.25a = 752.75 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
1.25c + 2.25(391 - c) = 752.75
1.25c + 879.75 - 2.25c = 752.75
c = 879.75 - 752.75
c = 127
Substitute c = 127 in eqn 1
a = 391 - 127
a = 264
Thus 127 children and 264 adults swam at the public pool that day
Joe tracked the height of his Dalmatian puppy from age 13 weeks to 25 weeks. He graphed the data and determined the line of best fit is y = 1.12x + 28.78 where x is the age in weeks and y is the height in centimeters. How old was the puppy when he was 54 centimeters tall? Round to the nearest tenth.
a. 22.5 weeks
b. 28.2
c. 73.9
d. 89.3
Answer:
22.5 weeks
Step-by-step explanation:
y = 1.12x + 28.78 represents the height of the puppy. Here that height is 54 cm:
Then 54 = y = 1.12x + 28.78
Combining the constants, we get 1.12x = 25.22. Dividing both sides by 1.12, x turns out to be 22.5 weeks.
If the total surface area of a cube is 302.46ft2 what best describes the length of the side of the cube?
Answer:
7.1ft
Step-by-step explanation:
The formula for calculating the total surface area of a cube is 2(L²+L²+L²)
=2(3L²)
= 6L²
Where L is the length of the cube
If the total surface area of a cube is 302.46ft², then
302.46 = 6L²
L² = 302.46/6
L² = 50.41
L =√50.41
L = 7.1ft
The length of the side of the cube is 7.1ft
The length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
To find the length of the side of a cube given its total surface area, we need to use the formula for the surface area of a cube.
The formula for the surface area of a cube is:
[tex]\[ \text{Surface Area} = 6s^2 \][/tex]
where s is the length of a side of the cube.
Given the total surface area is [tex]\( 302.46 \, \text{ft}^2 \)[/tex], we can set up the equation:
[tex]\[ 6s^2 = 302.46 \][/tex]
To solve for s we first divide both sides by 6:
[tex]\[ s^2 = \frac{302.46}{6} \][/tex]
[tex]\[ s^2 = 50.41 \][/tex]
Next, we take the square root of both sides to find s
[tex]\[ s = \sqrt{50.41} \][/tex]
[tex]\[ s \approx 7.1 \, \text{ft} \][/tex]
Thus, the length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
A certain drink is made by adding 4 parts water to 2.5 part drink mix. What percent of the mixture is water? Omit % sign in your answer. Round your answer to the nearest tenth.
The mixture contains 61.5% of water.
Step-by-step explanation:
Total parts = 4+ 2.5 = 6.5
Parts of water =4
parts of drink = 2.5
Percent of water in the mixture = 4 × 100/ 6.5
= 400/6.5
= 61.53%
It is rounded to the nearest tenth as 61.5%.
To find the percentage of water in the mix, we calculate the proportion of water (4 parts) to the total mixture (6.5 parts) and multiply by 100%, resulting in approximately 61.5%.
To determine what percent of the mixture is water when a drink is made with 4 parts water and 2.5 parts drink mix, we add together the parts of water and drink mix to find the total parts of the mixture. Then, we calculate the fraction of the mixture that is water and convert that to a percentage.
First, we find the total parts of the mixture:
Water: 4 parts
Drink mix: 2.5 parts
Total parts: 4 + 2.5 = 6.5 parts
Next, we calculate the percentage of the mixture that is water:
(Parts of water / Total parts) × 100%
(4 parts / 6.5 parts) × 100% \approximately 61.5%
Rounding to the nearest tenth, we get:
61.5
Claire is that in the first five years between 1977 in 1980 to the hospital about $12 per year are in the second five years between 1983 in 1888 the causal only by about two dollars a year show that Claire is correct
Answer:
Step-by-step explanation:
Can u solve 7-12 and 14 please
Answer:
1. 19
Step-by-step explanation:
Simplify: (-7x^2y^4)(-2x^3y^4)
Answer: 14x^5y^8
Step-by-step explanation:
(-7x^2y^4)(-2x^3y^4)
-7x^2y^4*-2x^3y^4, next take out the constants
−(7×−2)x^2x^3y^4y^4, -(7*-2)=14, so now you just need to add the variables.
(x^2+x^3)+(y^4+y^4)=x^5y^8
14x^5y^8
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
Solve the quadratic:
2X^2-64=0
Answer:
do you mean x=7
Step-by-step explanation:
this aint a quadratic function a qaudratic function is ax^2+bx+c=c
Find the measure of θ. (to the nearest tenth)
A) 16.2°
B) 16.8°
C) 17.1°
D) 17.9°
Answer: D
Step-by-step explanation:
On USA test prep the answer is D.
Answer:
They are incorrect. The answer is actually 36.9
Step-by-step explanation:
What's 0 divided by 0?
Answer:
Nothing
Step-by-step explanation:
You can't divide by zero
Answer:
ANYTHING DIVIDED BY 0 IS ALWAYS ZERO
Step-by-step explanation:
PLEASE MARK BRAINLIEST
brand A granola is 25% nuts and dried fruit and brand B granola is 10% nuts and dried fruit. how much of sweet item A and sweet item B should be mixed to form a 30-lb batch of sweets that is 22% nuts and dried fruit?
To create a 30-lb batch of sweets that is 22% nuts and dried fruit, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B.
To find the solution, we can set up a system of equations based on the percentages of nuts and dried fruit in each brand of granola and the desired final percentage.
Let x represent the amount of sweet item A (in pounds) and y represent the amount of sweet item B (in pounds) to be mixed.
The total weight of the mixture is x + y = 30 lbs.
The percentage of nuts and dried fruit in brand A is 25%, so the amount of nuts and dried fruit from A is 0.25x lbs.
The percentage of nuts and dried fruit in brand B is 10%, so the amount of nuts and dried fruit from B is 0.10y lbs.
The desired final percentage in the mixture is 22%, so we have the equation: (0.25x + 0.10y) / 30 = 0.22.
Now, we can solve this system of equations to find x and y.
First, we'll multiply the last equation by 30 to get 0.25x + 0.10y = 6.6.
Then, we can use substitution or elimination to solve for x and y.
In this case, it's simpler to use elimination, and we find that x = 12 lbs and y = 18 lbs.
Therefore, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B to create the desired 30-lb batch with 22% nuts and dried fruit.
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The figure on the right is made up of 5 squares.
Each side of the square is 7 cm.
What is the area of the figure?
Answer: [tex]245cm^{2}[/tex]
Step-by-step explanation:
The formula for calculating the area of a square is given by :
Area = [tex]l^{2}[/tex]
where [tex]l[/tex] is the length of a side .
Therefore , the area of one of the square given implies :
Area = [tex]7^{2}[/tex]
Area [tex]= 49[/tex]
And since there are 5 squares in all , the area will therefore be :
Area = [tex]5[/tex] x[tex]49[/tex]
Area = [tex]245cm^{2}[/tex]
Therefore: the area of the shape is [tex]245cm^{2}[/tex]
Write this decimal in number, thirty-nine thousandths
Answer:
0.039
Step-by-step explanation:
What is the slope of the line that contains the
coordinate points (8, -3) and (-2, 7)?
220x219
Answer:
-1
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(-2 - 8)
= (7+3)/(-10)
= 10/(-10) = -1
Which summation formula represents the series below? 1 + 2 + 6 + 24
Question:
Which summation formula represents the series below? 1 + 2 + 6 + 24
(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]
(b) [tex]\sum_{n=0}^{3} n ![/tex]
(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]
(d) [tex]\sum_{n=2}^{5} n ![/tex]
Answer:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.
Explanation:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]
Subtracting, we have,
[tex]1 !+2!+3 !+4 ![/tex]
Expanding the factorial,
[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]
Simplifying, we get,
[tex]1+2+6+24[/tex]
Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]
Hence, Option a is the correct answer.
Option b: [tex]\sum_{n=0}^{3} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]0!+1!+2!+3![/tex]
Expanding the factorial,
[tex]0+1+(2*1)+(3*2*1)[/tex]
Simplifying, we get,
[tex]0+1+2+6[/tex]
Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option b is not the correct answer.
Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]
Adding, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option c is not the correct answer.
Option d: [tex]\sum_{n=2}^{5} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option d is not the correct answer.
Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
Answer: A
Step-by-step explanation:
Solve the equation for 3y-4=6-2y
To solve the equation, you need to isolate/get "y" by itself in the equation:
3y - 4 = 6 - 2y Add 2y on both sides
3y + 2y - 4 = 6 - 2y + 2y
5y - 4 = 6 Add 4 on both sides
5y - 4 + 4 = 6 + 4
5y = 10 Divide 5 on both sides
[tex]\frac{5y}{5} =\frac{10}{5}[/tex]
y = 2
PROOF
3y - 4 = 6 - 2y Substitute/plug in 2 for y
3(2) - 4 = 6 - 2(2)
6 - 4 = 6 - 4
2 = 2
After Solving the equation for 3y-4=6-2y, we get y = 2. We must isolate the variable y on one side of the equation in order to get the solution to the equation 3y - 4 = 6 - 2y. Here's a step-by-step procedure:
Start by solving 3y - 4 = 6 - 2y, which is the provided problem.
Add 2y to both sides of similar phrases to combine them: 3y + 2y - 4 = 6 - 2y + 2y.
Simply put, this is: 5y - 4 = 6.
Add 4 to both sides of the variable word to isolate it: 5y - 4 + 4 = 6 + 4.
This may be summarised as 5y = 10.
To find y, multiply both sides of the equation by 5. (5y) / 5 = 10 / 5.
This may be condensed to: y = 2.
Consequently, y = 2 is the answer to the equation 3y - 4 = 6 - 2y.
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lonnie bought 6 pieces of ribbon. Each ribbon was 2 and 3/4 yards long. How much ribbon did Lonnie buy in all
Answer:
14.04
Step-by-step explanation:
you mupltiy
Answer:
b
Step-by-step explanation:
2.34 x 6 = 14.04
so it would total up to 14.12
find the value of x.
13,15,17,x,20,21; The median is 18.
Answer:
1
Step-by-step explanation:
13 15 17 x 20 21
Cross out all outer numbers
We are left with 17 and x
With double medians, you add those two together and then divide them by two.
With the median (total) being 18, we will first add 17+x then divide Y/2 = 18
The value of x is 1
Does Y+7=2x and
2y=4x-14 have a solution?
Answer: It has no exact solution
If the radius of the smaller sphere is 3 inches and the radius of the larger sphere is 6 inches how many times greater is the volume of the larger sphere
Answer:
8
Step-by-step explanation:
The formula of volume is 4/3 × π × radius3.
volume of smaller sphere = 4/3 x 3.14 x 3*3*3
v = 113.04
volume of larger sphere = 4/3 x 3.14 x 6*6*6
v = 904.32
904.32 / 113.04 = 8
The Answer Is 8 times
A steel ball is traveling through water with a speed of x meters per second, where x is positive the drag force, F
At what speed in meters per second does the ball have a force of 0.5 N on it
the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
To find the speed at which the drag force F on the steel ball is 0.5 N, we need to solve the equation:
[tex]\[ F = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Given that [tex]\( F = 0.5 \)[/tex], we can substitute this value into the equation and solve for x:
[tex]\[ 0.5 = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Subtracting \( 0.5 \) from both sides, we get:
[tex]\[ 0 = 0.004(x + 50)(x - 2.5) \][/tex]
Now, since the product of two factors is equal to zero, at least one of the factors must be zero. So we have:
[tex]\[ x + 50 = 0 \][/tex] or [tex]\[ x - 2.5 = 0 \][/tex]
Solving these equations:
1. [tex]\( x + 50 = 0 \)[/tex]
[tex]\[ x = -50 \][/tex]
2. [tex]\( x - 2.5 = 0 \)[/tex]
[tex]\[ x = 2.5 \][/tex]
Since the speed cannot be negative, the only valid solution is [tex]\( x = 2.5 \)[/tex] meters per second.
Therefore, the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
The complete Question is given below:
A steel ball is traveling through water with a speed of x meters per second, where x is positive. The drag force, F , in newtons (N) is: F=0.5+0.004(x+50)(x-2.5) At what speed in meters per second does the ball have a force of 0.5N on it?
5 1/2 of 2 1/3 is what number?
Answer:
19 1/4
Step-by-step explanation:
5 1/2 of 2 1/3
Change mixed fraction to improper fraction
11/2 of 7/2
Of means multiplication
11/2 x 7/2
77/4
19 1/4
Anusha needs to find a rectangular container large enough to hold a volume of 130 in.3. Which container should she use?
A. a container with the dimensions 2 by 5 by 10 inches
B. a container with the dimensions 3 by 4 by 10 inches
C. a container with the dimensions 3 by 5 by 10 inches
D. a container with the dimensions 4 by 2 by 10 inches
PLEASE HELP!!
Option C
Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Solution:
Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches
The volume of rectangular container is:
[tex]volume = length \times width \times height[/tex]
Option A
Container with the dimensions 2 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 2 \times 5 \times 10 = 100[/tex]
Thus volume is 100 cubic inches
Option B
Container with the dimensions 3 by 4 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 4 \times 10 = 120[/tex]
Thus volume is 120 cubic inches
Option C
Container with the dimensions 3 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 5 \times 10 = 150[/tex]
Thus volume is 150 cubic inches
Option D
Container with the dimensions 4 by 2 by 10 inches
Therefore, volume is given as:
[tex]Volume= 4 \times 2 \times 10 = 80[/tex]
Thus volume is 80 cubic inches
Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Answer:C. a container with the dimensions by 5 by 10 inches
V=15.81 V, P = 500 mW, I=
Answer:
0.032 Amperes
Step-by-step explanation:
in this question We are given;
Voltage, V =15.81 VPower, P = 500 mW (Milli-watts)We are required to determine the current, I
We need to know that power, P is given by the product of current and voltage.
That is;
Power = VI
But; 1 mW = 0.001 Watts
Thus, 500 mW = 0.5 watts
Rearranging the formula;
I = Power ÷ V
= 0.5 watts ÷ 15.81 V
= 0.0316 Amperes
= 0.032 A
Thus, the current, I is 0.032 Amperes
I need help please and thank you
Answer: [tex]Perimeter= 71.75[/tex]
The parameter of a 2-D figure is the total length of its boundaries.
Step-by-step explanation:
In the given figure a hexagon is given with the length of its sides given in mixed fraction.
A mixed fraction can be solved by [tex]p\frac{x}{y} =\frac{(p*y)+x}{y}[/tex]
So adding the given sides in the figure:
[tex]Perimeter=14\frac{3}{4}+ 4\frac{1}{2}+ 8\frac{1}{2}+10 \frac{2}{5}+10 \frac{2}{5}+12 \frac{4}{5}[/tex]
[tex]=\frac{(14*4)+3}{4} +\frac{(4*2)+1}{2} +\frac{(8*2)+1}{2} +\frac{(10*5)+2}{5}+ \frac{(10*5)+2}{5} +\frac{(12*5)+4}{5}[/tex]
[tex]=\frac{59}{4}+ \frac{9}{2}+ \frac{17}{2}+ \frac{52}{5}+ \frac{52}{5}+ \frac{64}{5}[/tex]
[tex]=14.75+4.5+8.5+10.4+10.4+12.8[/tex]
[tex]Perimeter= 71.75[/tex]
The perimeter of the given figure is 71.75
What is this (20+25)/3
Answer:
78 witch is 15%
Step-by-step explanation:
BRAINLIEST 60 POINTS!! PLEASE HELP ITS DUE TODAY
First image is for question 1, and second image is for question 2
1. Remember what we know about vertical angles and solve for x.
2. Use the figure to answer the questions.
(a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain.
Answer:
1.[tex]x^\circ= 7^\circ[/tex]
2.(a)Therefore , Side LJ =side CA
(b) BC = KL
Step-by-step explanation:
1.
we know that, vertically opposite angles are congruent .
[tex]\therefore (x+16)^\circ= (4x-5)^\circ[/tex]
[tex]\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ[/tex]
[tex]\Leftrightarrow 3x^\circ= 21^\circ[/tex]
[tex]\Leftrightarrow x^\circ= 7^\circ[/tex]
2.
(a)SAS = side,angle , side
Given ,side AB = side KJ
and ∠CAB= ∠LJK
All Pythagorean Triples are unique.
Since side AB = side KJ
Therefore , Side LJ =side CA
It satisfies SAS postulate ThereforeΔABC≅ΔKJL
(b)
HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.
Since,
All Pythagorean Triples are unique.
Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL
Which expression is equivalent to 4√147
A. 28√3
B. 12√7
C. 3√7
Answer:
A) 28*sqrt(3)
Step-by-step explanation:
Answer:
28√3 is your answer
Step-by-step explanation:
A building has the shape of a pyramid within a square base. The mid segment parallel to the ground of each triangular face of the pyramid has a length of 58 feet. Find the length of the base the pyramid.
Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)
Final answer:
The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.
Explanation:
The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.
Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.
This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.